Quantum thermodynamics -- Bridging the gap between resource theories and the theory of open quantum systems

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The theory of thermodynamics teaches us something about the fundamental limits of nature. It predicts an arrow of time and allows to understand complicated machines in terms of a few parameters. Deriving and understanding the laws of thermodynamics for small and strongly fluctuating quantum engines presents one of the most important and fascinating research directions nowadays. At the moment there are two seemingly unrelated research directions in quantum thermodynamics. On the one hand, one follows the tradition of open quantum system theory to study the dynamics of a small quantum system under the influence of its environment (e.g., a heat bath at temperature T or an external laser field). Then, using arguments from statistical mechanics, it is possible under certain conditions to derive the laws of thermodynamics which hold even for strongly fluctuating systems arbitrarily far away from equilibrium. Many of these predictions have been also experimentally verified. On the other hand, within the so-called "resource theory" approach one does not start with a detailed microscopic description, but one rather studies specific transformations which fulfill elementary physical principles (e.g., energy conservation). Given this set of transformations one then studies how certain resources can be converted into each other (e.g., how much heat can be converted into work or which nonequilibrium states can be transformed). Unfortunately, the resulting framework, which uses many insights from quantum information theory, is very abstract and hard to implement experimentally. At present it is unclear as to whether the assumptions used in the first approach are compatible with the second approach and vice versa. There is no fruitful link between both theories so far and this project aims at closing this gap. It aims at exploring mainly two questions. First, how realistic are the assumptions of resource theories, can they be fulfilled in experiments and is it possible to translate them into the context of open quantum system theory? Second, after having answered the first question, can we use the insights from resource theoretic studies to learn more about the thermodynamics of open quantum systems?